This talk is devoted to confront two different approaches to the problem of dynamic perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary conditions. Using variational methods, we show the well-posedness of this problem in a suitable measure theoretic setting. We prove that this unique variational solution actually coincides with the unique entropic solution of the hyperbolic formulation. Finally, thanks to the finite speed propagation property, we establish a new short time regularity result for the solution.